Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T20:00:38.389Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of the polarization driftin a strongly magnetized plasma

Published online by Cambridge University Press:  03 February 2012

Daniel Han-Kwan
Daniel Han-Kwan*
Affiliation:
École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d’Ulm, 75230 Paris Cedex 05 France. daniel.han-kwan@ens.fr
Get access

Abstract

We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fine scales. We give a new interpretation of the asymptotic equations obtained by Frénod and Sonnendrücker [SIAM J. Math. Anal. 32 (2001) 1227–1247] when the intensity of the magnetic field goes to infinity. We introduce the so-called polarization drift and show that its contribution is not negligible in the limit, contrary to what is usually said. This is due to the non linear coupling between the Vlasov and Poisson equations.

Keywords

Vlasov-Poisson equationstrong magnetic field regimefinite Larmor radius scalingelectric driftpolarization driftoscillations in time
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012 , pp. 929 - 947
Copyright
© EDP Sciences, SMAI, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Allaire, G., Homogenization and two-scale convergence. SIAM J. Math. Anal. XXIII (1992) 1482–1518. Google Scholar
Arsenev, A.A., Existence in the large of a weak solution of Vlasov’s system of equations. Z. Vychisl. Mat. Mat. Fiz. 15 (1975) 136–147. Google Scholar
Bostan, M., The Vlasov-Poisson system with strong external magnetic field. Finite Larmor radius regime. Asymptot. Anal. 61 (2009) 91–123. Google Scholar
Degond, P., Global existence of smooth solutions for the Vlasov-Fokker-Planck equations in 1 and 2 space dimensions. Ann. Sci. École Norm. Sup. 19 (1986) 519–542. Google Scholar
Frénod, E. and Mouton, A., Two-dimensional finite Larmor radius approximation in canonical gyrokinetic coordinates. J. Pure Appl. Math. : Adv. Appl. 4 (2010) 135–166. Google Scholar
Frénod, E. and Sonnendrücker, E., The finite Larmor radius approximation. SIAM J. Math. Anal. 32 (2001) 1227–1247. Google Scholar
Frénod, E., Mouton, A. and Sonnendrücker, E., Two-scale numerical simulation of the weakly compressible 1D isentropic Euler equations. Numer. Math. 108 (2007) 263–293. Google Scholar
Frénod, E., Salvarani, F. and Sonnendrücker, E., Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method. Math. Models Methods Appl. Sci. 19 (2009) 175–197. Google Scholar
Ghendrih, P., Hauray, M. and Nouri, A., Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions. KRM 2 (2009) 707–725. Google Scholar
Golse, F. and Saint-Raymond, L., The Vlasov-Poisson system with strong magnetic field. J. Math. Pures Appl. 78 (1999) 791–817. Google Scholar
Grandgirard, V. et al., Global full-f gyrokinetic simulations of plasma turbulence. Plasma Phys. Control. Fusion 49 (2007) 173–182. Google Scholar
Han-Kwan, D., The three-dimensional finite Larmor radius approximation. Asymptot. Anal. 66 (2010) 9–33. Google Scholar
D. Han-Kwan, On the three-dimensional finite Larmor radius approximation : the case of electrons in a fixed background of ions. Submitted (2010).
Lin, Z., Ethier, S., Hahm, T.S. and Tang, W.M., Size scaling of turbulent transport in magnetically confined plasmas. Phys. Rev. Lett. 88 (2002) 195004-1–195004-4. Google ScholarPubMed
Lions, P.L. and Perthame, B., Propagation of moments and regularity for the three-dimensional Vlasov-Poisson system. Invent. Math. 105 (1991) 415–430. Google Scholar
Mouton, A., Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel. KRM 2 (2009) 251–274. Google Scholar
Nguetseng, G., A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. Google Scholar
Ukai, S. and Okabe, T., On classical solutions in the large in time of two-dimensional Vlasov’s equation. Osaka J. Math. 15 (1978) 245–261. Google Scholar
J. Wesson, Tokamaks.Clarendon Press-Oxford (2004).